Pseudo-linear machine models based on time-varying inductance matrix are theoretically correct only when the media, in which the electromagnetic field exists, can be assumed linear. Exclusively in such a case indeed, the n fluxes linked with each of the n windings are correctly expressible as linear combinations of the n currents in their whole domain. Any attempt to improve such models, aimed at incorporating the non-linear behavior, is theoretically not correct, even if it leads to acceptable quantitative results in some operating conditions. Such improved models can generate heavily mistaken results if one pretends to extend them beyond their usual scope of validity.
In substance, the correct modeling of electric machines, accounting also for magnetic non linearities and/or presence of permanent magnets, demands from the very beginning that the theoretical and procedural approach be radically different from the ones still widely used today, which represented the almost unique practicable way in absence of powerful computers.
DE4115338A1 discloses a control device capable of detecting and/or regulating position or angular velocity of a rotor of an electrical machine by using a Kalman filter.